Distorted-wave theory of electron-ion collisions. I. Direct excitation and ionization

Abstract

A simple modification of the Bethe approximation for high-energy electron-atom collisions is considered for the purpose of analyzing the medium-energy scattering by highly stripped ionic targets. The effect of amplitude and phase distortions of the projectile-electron wave function on the excitation and ionization cross sections is approximately taken into account using the Elwert factor and the eikonal procedure, respectively. To facilitate the cross-section calculation further, the momentum-transfer-dependent part in the excitation matrix element is factored out in terms of an average transfer. The energy dependence of the various modification factors is studied in detail, showing that the distortion effect is large for ionic targets and decays only slowly with the scattering energy, as $E^{-\frac{1}{2}}$. For a neutral target, however, the distortion effects roughly cancel with each other, thus resulting in the effectiveness of the unmodified Bethe cross section at much lower energies than one usually expects. The improved formalism is applied to estimate the total cross sections for the direct excitation and ionization of outer-shell electrons of the ionic target. The results are drastically changed from the unmodified Bethe approximation, and are generally in fair agreement with experimental data for all energies except in the threshold region.